This thesis explores the ADRs in Taiwan and Japan and examines their return and volatility transmission dynamics with vector autoregressive (VAR) and vector error correction (VEC) models. We find some major differences between Taiwanese and Japanese ADRs Furthermore, the cross-correlation function (CCF) is used to test the causality in variance.The results show that the transmission of the underlying stock return is the strongest reason for the variance of ADRs returns. Compared to Japan, S&P 500 index return has a stronger impact on the Taiwanese ADRs. Besides, there is a two-way feedback relation between ADRs returns and underlying stock returns. However, the latter generally leads the former. Also, exchange rate returns have another two-way feedback with ADRs, but S&P 500 index returns do not exist lead-lag relation with ADR returns.There is volatility spillover effect between Taiwanese ADRs and their underlying stock, and so are Japanese ADRs and their underlying stock. The duration of the spillover effect of Japanese ADRs is not as long as that of Taiwanese ADRs, and the reason might be that the Japanese market is more efficient. Taiwanese ADRs and S&P 500 index have volatility spillover effect on the same calendar day only, and they are not as significant in Japan. Finally, the volatility spillover effects between ADRs and exchange rates are not significant.